The electrophoresis of X-DNA is observed in a microscale converging channel where the center-of-masses trajectories of DNA molecules are tracked to measure instantaneous electrophoretic (EP) mobilities of DNA molecules of various stretch lengths and conformations. Contrary to the usual assumption that DNA mobility is a constant, independent of field and DNA length in free solution, we find DNA EP mobility varies along the axis in the contracting geometry. We correlate this mobility variation with the local stretch and conformational changes of the DNA, which are induced by the electric field gradient produced by the contraction. A "shish-kebab" model of a rigid polymer segment is developed, which consists of aligned spheres acting as charge and drag centers. The EP mobility of the shish-kebab is obtained by determining the electrohydrodynamic interactions of aligned spheres driven by the electric field. Multiple shish-kebabs are then connected end-to-end to form a freely jointed chain model for a flexible DNA chain. DNA EP mobility is finally obtained as an ensemble average over the shish-kebab orientations that are biased to match the overall stretch of the DNA chain. Using physically reasonable parameters, the model agrees well with experimental results for the dependence of EP mobility on stretch and conformation. We find that the magnitude of the EP mobility increases with DNA stretch, and that this increase is more pronounced for folded conformations.